Question

classifying a triangle
on the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft × 15 ft × 17 ft. without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle, or an obtuse triangle.
using the tools from this lesson, you determine that the general shape of the sail is a(n) triangle

Explanation:

Step1: Recall the Pythagorean - related rules

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), it's a right - triangle; if \(a^{2}+b^{2}>c^{2}\), it's an acute - triangle; if \(a^{2}+b^{2}

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

\(a^{2}+b^{2}=7^{2}+15^{2}=49 + 225=274\), and \(c^{2}=17^{2}=289\).

Step3: Compare the values

Since \(274<289\), i.e., \(a^{2}+b^{2}

Answer:

obtuse